Chapter 229 The Tool Is Still Easy to Use

"neither?"

Molina froze.

She calmed down, looked at Lu Zhou, and said in a suspicious tone: "I know you are a genius... Although Goldbach's conjecture is not my research field, if I heard correctly, you are not planning to use this The work of a century must be overturned and redone?"

Lu Zhou smiled lightly and said in a relaxed tone.

"The problem of a+b is ultimately a complex formulation of Goldbach's conjecture, that is, every large even number N can be expressed as A+B, where the number of prime factors of A and B does not exceed a and b respectively. When a=b=1, this problem will eventually return to the original statement, that is, any even number greater than 2 can be written as the sum of two prime numbers.”

The number of prime factors is 1, so it is naturally a prime number.

So the form of 1+1 is, after all, Goldbach's conjecture itself.

Molina said in a teasing tone, "You mean that in this century, people who have studied Goldbach's conjecture have been doing useless work?"

"Of course not," Lu Zhou shook his head, and suddenly asked a question she didn't expect, "Do you know anything about sports?"

Molina froze slightly, frowned and said, "Sports?"

Lu Zhou: "You know the long jump."

Molina curled her lips and said speechlessly, "Of course."

Lu Zhou smiled lightly and said: "The a+b proof method opened by Brown is equivalent to the run-up before the long jump. Although the run-up time itself is not included in the score, is the run-up useless? The same reason, a+b It is equivalent to the run-up of Goldbach's conjecture. If it is not because of it, there will be no subsequent large sieve method-this inspiring and potential analytical number theory research tool. It can even be said that the value of the large sieve method has been Beyond the Goldbach conjecture itself."

Regardless of whether the big sieve method can really cross the final 1+1, it has completed its historical mission and played an important role in analytic number theory.

Including Lu Zhou, have benefited a lot from it.

Flicking her long hair by her ear, Molina looked at Lu Zhou: "So, how do you plan to prove it?"

Lu Zhou's mouth evoked a confident smile.

"Of course, I use my own method to prove it."

do not know why.

Seeing the confident smile on his face, Molina's heart beat inexplicably accelerated for two seconds.

Of course, for a woman who has decided to marry mathematics, the so-called heartbeat is only a moment...

...

The solution of a mathematical conjecture requires the accumulation of workload and a creative genius.

Both are indispensable.

It's like Fermat's last theorem.

When Taniyama Shimura's conjecture is proved, although people can't see the specific prospect, everyone knows it, because a tool that can solve the problem has appeared. Sure enough, Andrew Wiles finally completed this historic work.

But for Goldbach's conjecture, neither the big sieve method nor the circle method has such a feeling.

The predecessors' work has done a lot of foreshadowing, but whether it is Chen's theorem from "9+9" to "1+2", or Helfgott's proof of Goldbach's weak conjecture under odd conditions, there is only one difference between last step. Even the significance of Chen's theorem is more to let other mathematicians understand that the big sieve method has been achieved by Chen Jingrun to the extreme, and this road is no longer feasible.

The same goes for circles.

It is precisely for the same reason that in his speech at the end of last year, Helfgott used "We still have a long way to go to fully prove Goldbach's conjecture" as his final concluding remarks, expressing his interest in the short-term There is no hope that Bach's conjecture cannot be solved within.

At least, no hope for the round method.

Lu Zhou couldn't help but start to reflect, whether these two methods have entered a dead end.

When he first studied the twin prime number conjecture, he also faced a similar problem.

Zhang Yitang's research cleverly selected the lambda function, and limited the distance between pairs of prime numbers to 70 million. The successors reduced this number to 246 within a year, and then they could not go any further.

Lu Zhou's original idea was to choose an appropriate lambda function, but after countless attempts, he finally found that this path did not work.

There are so many lambda functions to choose from, but no matter how hard he looks, he can't find the right one.

It wasn't until he tried a completely different way of proof in a heuristic state and introduced topology theory into the concept of sieve method that he opened the door to a new world.

Although this line of thought was first mentioned in Professor Zellberg's 1995 paper on the study of Goldbach's conjecture, it was himself who improved it and introduced it into the problem of pairs of prime numbers.

Later, Lu Zhou introduced the knowledge of group theory on this basis, pushed the pair of prime numbers with a finite distance to infinity, and solved the Polignac conjecture on this basis. This method has been modified twice. Unrecognizable, completely deviated from the original appearance of the sieve method.

Therefore, Lu Zhou engraved a new name on this weapon of his own, that is, "group construction method".

But when thinking about Goldbach's conjecture, inertial thinking made him selectively ignore his own tools.

On the surface, the group construction method seems to have nothing to do with Goldbach's conjecture, but it evolved from the sieve method at the root, and it always goes to solve the prime number problem.

As long as it is improved, it may not be impossible to use this tool for Goldbach's conjecture, which is also a prime number problem.

When this mathematical method is continuously improved, perfect enough to solve many problems, and perfected from a toothpick to a Swiss army knife, its meaning may no longer be a simple tool, but gradually evolve into a theoretical framework! And it is a theoretical framework in analytic number theory!

Just like Shinichi Mochizuki, a well-known "secondary disease" in the mathematics world, created the "Intercosmic Teichmüller Theory" and "Alien Arithmetic Holomorphic Structure" when studying the ABC conjecture.

Whether it is to establish a theory first and then prove the value of the theory, or to develop a novel theory while studying a specific mathematical problem, there are precedents to follow.

From Goldbach's conjecture, Lu Zhou vaguely saw hope.

...

After coming out of the eating club, Lu Zhou did not go to the library for a while after eating as usual, but went to the Princeton Institute for Advanced Study.

Although he didn't make an appointment, according to Professor Delin himself, if nothing else happens, he will be here every night from 6:00 to 8:00.

Knocking on the door of the office, Lu Zhou walked in.

Stopping the ballpoint pen in his hand, Professor Deligne looked at Lu Zhou who was standing across the desk, and asked in a relaxed tone.

"Have you considered it?"

Lu Zhou nodded and said.

"Yes, I plan to continue to complete my research... Sorry, I may not be able to spare extra energy to join your project."

Deligne nodded, not dissatisfied with it.

Sitting in his position, it is difficult to be narrow-minded like the boss of a doctoral student who uses some boring tests to test whether the students are "obedient". As he said at the beginning, he offered Lu Zhou two options.

Deligne: "I respect your choice, but as your tutor, I need to know what your research topic is?"

Lu Zhou answered truthfully: "Goldbach's conjecture."

Deligne nodded, and did not express surprise at his research topic like Molina did. The ordinary calmness on his face surprised Lu Zhou who threw out this proposition.

Could it be...

Senior Deligne also believes that he is the "best candidate" to solve this conjecture?

What an embarrassment.

Lu Zhou felt a little proud.

Deligne: "Goldbach's conjecture is an interesting problem. I also studied it when I was young, but I didn't go deep into it. I may not be able to provide you with much help. At present, the closest international research results are Chen's theorem. and Helfgott's proof of the weak conjecture, and I look forward to seeing something novel from you based on it."

"Of course, in addition to your own research, I also have some work outside of research that needs you to do. For example, teaching assistants and the like."

Lu Zhou nodded: "No problem... If it is a course on number theory or functional analysis, I can still teach some."

"It's mainly analytic number theory. I believe that with your ability, you are more than sufficient for this job... In addition, I have prepared a meeting gift for you."

After a pause, the old Mr. Deligne stretched out his hand and opened the drawer, took out a certificate-like thing from it, and put it on the table, a smile softened on his serious face.

"I heard from you that your family's conditions are not good. When I helped you with the admission procedures yesterday, I helped you solve the problem of bursaries. You can take this thing to the academic affairs later. The matter of tuition fees has been settled."